Concept
Distinguish variation in cases from uncertainty in a mean
Customers can have wildly different experiences while the average is estimated very precisely.
When it fits
- A chart or report labels an error bar without explaining what it measures.
When to avoid it
- The familiar standard-error formula for a mean assumes an appropriate independent-sample model.
The idea
Standard deviation describes variation among observations. Standard error describes uncertainty in an estimator such as a mean. They answer different questions. Ask which quantity the bars show before concluding that individual results are consistent or that the mean is uncertain.
An example
Thousands of widely varying delivery times can produce a narrow confidence interval for the mean without making any individual delivery predictable.
Check your result
The explanation matches the kind of uncertainty actually displayed.
Keep this limit in mind
- The familiar standard-error formula for a mean assumes an appropriate independent-sample model.
Connected ideas
Useful withRead a confidence interval as a procedure with assumptions
Evidence and sources
Supports
For an independent sample mean under the usual model, its estimated standard error is the sample standard deviation divided by the square root of the sample count.
Correlated, weighted or complex samples do not automatically follow this formula.
Confidence Limits for the Mean · Confidence-limit formula